Search: id:A011800
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%I A011800
%S A011800 1,1,2,7,34,206,1486,12412,117692,1248004,14625856,187638716,
%T A011800 2614602112,39310384192,634148436104,10923398137576,200069534481616,
%U A011800 3882002527006352,79535575126745632,1715658099715217584
%N A011800 Number of labeled forests of n nodes each component of which is a path.
%D A011800 R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see 
               Problem 5.15(d).
%H A011800 T. D. Noe, <a href="b011800.txt">Table of n, a(n) for n=0..100</a>
%F A011800 E.g.f.: exp[ x+x^2/(2(1-x)) ].
%F A011800 a(n) = Sum_{k=0..n} |Stirling1(n, k)|*A003724(k). - Vladeta Jovovic (vladeta(AT)eunet.rs), 
               Oct 19 2003
%t A011800 Function[ esl, esl*Array[ Factorial, Length[ esl ], 0 ] ][ CoefficientList[ 
               Series[ Exp[ x+x^2/(2-2x) ], {x, 0, 20} ], x ] ] (from Olivier Gerard).
%Y A011800 Sequence in context: A145345 A056543 A075834 this_sequence A112916 A145845 
               A002720
%Y A011800 Adjacent sequences: A011797 A011798 A011799 this_sequence A011801 A011802 
               A011803
%K A011800 nonn,easy,nice
%O A011800 0,3
%A A011800 Herbert S. Wilf (wilf(AT)math.upenn.edu)

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